Start from scratch.
Remove/Sign Out of the Apple ID on the iPhone in Messages only
Sign Out of the Apple ID on the Mac.
Turn the App Off on the iPhone
Quit the app on the Mac.
Open the app on the iPhone and wait for the number to verify.
Open the Mac version and add back the Apple ID
On the Mac Version start a New Message and Add the iPhone Number in full including Country Code.
If that does not appear on the iPhone go here When the iMessages account will not Login
The last section on Phoning Apple can be very long winded to get up the chain of responders until someone can and will look at the server.
If it worked then Add the Apple ID back to the iPhone.
This should cause a pop on the Mac which you needs to accepts to link the two IDs for syncing iMessages.
Make sure the iPhone and Mac are on the same LAN
That means the iPhone needs to have the WiFi On and have joined the network.
Enable Text Forwarding
Choose the Mac and it should get a Code Number to appear on the Mac which needs entering back on the iPhone.
9:17 pm Thursday; November 16, 2017
iMac 2.5Ghz i5 2011 (Sierra)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
iPhone 6 iOS 11.x and an iPad (2)